a$.$What is the duration of a two$-$year bond that pays an annual coupon of $10$ percent and has a current yield to maturity of $12$ percent? Use $$1,000$ as the face value.

Note: Do not round intermediate calculations. Round your answer to $4$ decimal places. $($e$.$g$.,32\mathrm{.}1616)$

b$.$What is the duration of a two$-$year zero$-$coupon bond that is yielding $11\mathrm{.}5$ percent? Use $$1,000$ as the face value.